We need to analyze the tumor micro array data from the Elements Of Statistical Learning. It has 14 subtypes of tumor cells. We need to use the SOM Algorithm to cluster the data into multiple groups.

library(kohonen)
## Warning: package 'kohonen' was built under R version 3.6.3
library(Umatrix)
## Warning: package 'Umatrix' was built under R version 3.6.3
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(ape)
## Warning: package 'ape' was built under R version 3.6.3
library(dendextend)
## Warning: package 'dendextend' was built under R version 3.6.3
## 
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##  To suppress this message use:  suppressPackageStartupMessages(library(dendextend))
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## 
## Attaching package: 'dendextend'
## The following objects are masked from 'package:ape':
## 
##     ladderize, rotate
## The following object is masked from 'package:stats':
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##     cutree
library(RColorBrewer)
library(scales)
df1 <- read.csv('nci.data.csv',sep=",",row.names=1,header = TRUE)

We first scale the data.

EigenValues <- eigen(cov(scale(df1)))
EigenValues$values
##  [1] 8.0957119 5.3797629 3.5583361 2.7208690 2.5096325 2.0444217 1.8296886
##  [8] 1.7528499 1.6115437 1.4860941 1.3443270 1.3216904 1.2671661 1.2168416
## [15] 1.1300098 1.0475872 1.0273544 0.9962967 0.9699703 0.9361556 0.8693644
## [22] 0.8621069 0.8323595 0.8037197 0.7926028 0.7645869 0.7440932 0.7356460
## [29] 0.7003424 0.6805286 0.6690675 0.6592918 0.6417513 0.6163924 0.5965587
## [36] 0.5798647 0.5741100 0.5487758 0.5305889 0.5299946 0.5128732 0.4968256
## [43] 0.4916484 0.4805703 0.4577736 0.4529224 0.4387011 0.4264547 0.4084076
## [50] 0.3811480 0.3749040 0.3643935 0.3466927 0.3349110 0.3211923 0.3018903
## [57] 0.2624658 0.2333543 0.2058479 0.1760215 0.1611637 0.1452791 0.1270222
## [64] 0.1194815
m <- apply(df1,2,mean)
s <- apply(df1,2,sd)
z <- scale(df1,m,s)

Now we turn the data into a matrix so that we can pass the data to the SOM Algorithm.

training_data <- as.matrix(z)

We need to apply SOM to the data and we know that the size of SOM is given by 5sqrt(N) Here N is the number of observation. So to break it down, If Columns are your feature and each row is one observation then Number of Nodes = 5 sqrt (# of Rows * # of columns).

We observe that there are 6830 Rows and 64 Columns. So the Number Of Observations can be summed up as:

nr <- nrow(z)
nc <- ncol(z)
s_lower <- 0.25*sqrt((nr*nc))
s_lower
## [1] 165.2876
s_upper <- 4*sqrt((nr*nc))
s_upper
## [1] 2644.602

The counts lot gives us the count of the number of states map into the different units.

coolBlueHotRed <- function(n,alpha=1){rainbow(n,end=4/6,alpha=alpha)[n:1]}
data_train_matrix <- training_data
som_grid <- somgrid(xdim = 10, ydim = 10, topo="hexagonal")
som_model <- som(data_train_matrix,grid=som_grid,rlen=1000)

The counts lot gives us the count of the number of states map into the different units.

plot(som_model,type="counts",palette.name=coolBlueHotRed)

We now plot the SOM amd specify the cutoff point at a location where we can observe the approximate cutoff in the Dendrogram plotted above.

By specifying the cutoff point obtained from the plot above and clustering the data at that height gives us the approximate distribution of the data into 3 clusters.

codes <- som_model$codes[[1]]
d <- dist(codes)
hc <- hclust(d)
som_cluster <- cutree(hc,k=14)
# plot these results:
my_pal <- (hue_pal()(14))
my_bhcol <- my_pal[som_cluster]

{plot(som_model,type="mapping",col="black",bgcol = my_bhcol)
  add.cluster.boundaries(som_model,som_cluster)}

show_col(my_pal)

We observe that the map that there are a large number of smaller clusters formed. This creates a large number of clusters ie., a large number of clusters are formed which is greater than our requirement of 14 clusters.

som_grid <- somgrid(xdim = 15, ydim = 15, topo="hexagonal")
som_model <- som(data_train_matrix,grid=som_grid,rlen=1000)

The counts lot gives us the count of the number of states map into the different units.

plot(som_model,type="counts",palette.name=coolBlueHotRed)

We now plot the SOM amd specify the cutoff point at a location where we can observe the approximate cutoff in the Dendrogram plotted above.

By specifying the cutoff point obtained from the plot above and clustering the data at that height gives us the approximate distribution of the data into 3 clusters.

codes <- som_model$codes[[1]]
d <- dist(codes)
hc <- hclust(d)
som_cluster <- cutree(hc,k=14)
# plot these results:
my_pal <- (hue_pal()(14))
my_bhcol <- my_pal[som_cluster]

{plot(som_model,type="mapping",col="black",bgcol = my_bhcol)
  add.cluster.boundaries(som_model,som_cluster)}

show_col(my_pal)

We observe that the map that there are a large number of smaller clusters formed. This creates a large number of clusters ie., a large number of clusters are formed which is greater than our requirement of 14 clusters

som_grid <- somgrid(xdim = 20, ydim=20, topo="hexagonal")
som_model <- som(data_train_matrix,grid=som_grid,rlen=1000)

The counts lot gives us the count of the number of states map into the different units.

plot(som_model,type="counts",palette.name=coolBlueHotRed)

We now plot the SOM amd specify the cutoff point at a location where we can observe the approximate cutoff in the Dendrogram plotted above.

By specifying the cutoff point obtained from the plot above and clustering the data at that height gives us the approximate distribution of the data into 3 clusters.

codes <- som_model$codes[[1]]
d <- dist(codes)
hc <- hclust(d)
som_cluster <- cutree(hc,k=14)
# plot these results:
my_pal <- (hue_pal()(14))
my_bhcol <- my_pal[som_cluster]

{plot(som_model,type="mapping",col="black",bgcol = my_bhcol)
  add.cluster.boundaries(som_model,som_cluster)}

show_col(my_pal)

We observe that the map that there are a large number of smaller clusters formed. This creates a large number of clusters ie., a large number of clusters are formed which is greater than our requirement of 14 clusters

som_grid <- somgrid(xdim = 25, ydim=25, topo="hexagonal")
som_model <- som(data_train_matrix,grid=som_grid,rlen=1000)

The counts lot gives us the count of the number of states map into the different units.

plot(som_model,type="counts",palette.name=coolBlueHotRed)

We now plot the SOM amd specify the cutoff point at a location where we can observe the approximate cutoff in the Dendrogram plotted above.

By specifying the cutoff point obtained from the plot above and clustering the data at that height gives us the approximate distribution of the data into 3 clusters.

codes <- som_model$codes[[1]]
d <- dist(codes)
hc <- hclust(d)
som_cluster <- cutree(hc,k=14)
# plot these results:
my_pal <- (hue_pal()(14))
my_bhcol <- my_pal[som_cluster]

{plot(som_model,type="mapping",col="black",bgcol = my_bhcol)
  add.cluster.boundaries(som_model,som_cluster)}

show_col(my_pal)

This gives us the summary of the Self Organization Map.

summary(som_model)
## SOM of size 25x25 with a hexagonal topology and a bubble neighbourhood function.
## The number of data layers is 1.
## Distance measure(s) used: sumofsquares.
## Training data included: 6830 objects.
## Mean distance to the closest unit in the map: 29.468.

We now analyze the list of all the states and the prototypes that are closest to them.

head(som_model$unit.classif)
## [1] 337  87 112  87 207 171

We now analyze the relative changes of the prototype code book vectors as we proceed through 200 different iteration.

head(som_model$changes)
##            [,1]
## [1,] 0.01131829
## [2,] 0.01115900
## [3,] 0.01129722
## [4,] 0.01145146
## [5,] 0.01126453
## [6,] 0.01139310

We observe that the changes start decreasing as we start increasing the number of iterations. A better understanding can be obtained from the Graph which represents the changes in the prototype. The things start converging as we move in the iteration.

plot(som_model,type="changes",main="CRIME DATA")

We now plot the Codes plot which gives us the distribution of various crimes across various nodes.

plot(som_model,type = "codes")

We now plot the distance to the Neighbours between each states that are plotted into a particular node.

plot(som_model,type="dist.neighbours")

We now plot the componenet plane plots. Which Visualizes the original data over the SOM that we have created.

som_model$data <- data.frame(som_model$data)

{for (i in 1:50){
  plot(som_model, type = "property", property = codes[,i], main=names(som_model$data)[i],palette.name=coolBlueHotRed)
  }}

We find the distance using the SOM_Model codes and observe a clear distinction between the height of the dendrogram between the 2 clusters. This helps us find the point for the cutoff and also helps us easily cluster the dat into 3 distinct groups which was difficult in the case of Plain Heirarchical Clustering using Eucledian Distance.

dend <- codes %>% dist %>%
  hclust %>% as.dendrogram %>%
  set("branches_k_color", k = 14) %>% set("branches_lwd", 0.7) %>%
  set("labels_cex", 0.6) %>% set("labels_colors", k = 14) %>%
  set("leaves_pch", 19) %>% set("leaves_cex", 0.5) 

ggd1 <- as.ggdend(dend)
ggplot(ggd1, horiz = TRUE)